We define the property of a series being convergent. We then prove theorems about convergent series. We also prove that the series you gave is not convergent. In particular, we don't define what the "sum" of a non-convergent series is. So, any discussion which assumes such a series has a "sum" is incorrect from the start.

Have a look at the link ..

http://www.maths.abdn.ac.uk/~igc/tch/ma2001/notes/node49.html  

--Last edited by zee on 2007-03-04 15:45:09 --